Creating a mesh on any object, duplicating the mesh and editing faces
So, assuming your problem is getting actual geometry out of the Dupli-Objects that you generate in the vertex-positions of your octahedron:






Create the object to be duplicated. In this example: the octahedron
Create the object whose vertices indicate the positions of the Dupli-Objects. In this example: the cube
Parent the octahedron to the cube
Set the Duplication Mode in the Object Tab to Verts
Select the object whose vertices position the clones (the cube)
Create actual geometry from the clones by using the Make Duplicates Real function